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Self-improvement of weighted pointwise inequalities on open sets

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arxiv 2002.11520 v1 pith:UT3R2F7F submitted 2020-02-25 math.CA math.AP

Sylvester Eriksson-Bique , Juha Lehrbäck , Antti V. Vähäkangas This is my paper · ORCID
classification math.CAmath.AP
keywords inequalitieshardypointwiseopenself-improvementweightedsetsweights
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abstract

We prove a general self-improvement property for a family of weighted pointwise inequalities on open sets, including pointwise Hardy inequalities with distance weights. For this purpose we introduce and study the classes of $p$-Poincar\'e and $p$-Hardy weights for an open set $\Omega\subset X$, where $X$ is a metric measure space. We also apply the self-improvement of weighted pointwise Hardy inequalities in connection with usual integral versions of Hardy inequalities.

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Cited by 1 Pith paper

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  1. A Contrastive Diffusion-based Network (CDNet) for Time Series Classification

    cs.LG 2025-07 reject novelty 5.0 of 10

    CDNet generates contrastive training pairs via CNN-based diffusion transitions between time series samples and claims consistent accuracy gains for deep classifiers on binary UCR datasets.

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